Given the role played by all symmetries of MLE for the existence of null HR knots, one may wish to retain as much as may be feasible all those same
symmetries for a NLE theory. Besides the usual MLE theory, a recent result[1]} has established that there exist only two other possible NLE theories
which preserve exactly all the same symmetries of spacetime Poincaré and conformal invariance and of electromagnetic duality between
the electric and magnetic sectors. One of these NLE theories, dubbed BB electrodynamics by the authors of Ref.[1]}
(for Bialynicki-Birula[3]}), corresponds to a Hamiltonian density given as \({\cal H}_{BB}=|\vec{D}\times \vec{B}|\) .
The other, dubbed ModMax theories by their discoverers[1]},
corresponds to a continuous deformation of MLE parametrised by a single real and positive parameter, \(\gamma \ge 0\) ,
which reduces to MLE for \(\gamma =0\) , and of which the Lagrangian density is uniquely given by[1]}, [6]},
\({\cal L}_\gamma ({\cal S},{\cal P}) &=& \cosh \gamma \,{\cal S}\,+\,\sinh \gamma \,\sqrt{{\cal S}^2+{\cal P}^2} \nonumber \\&=& \frac{1}{2}\cosh \gamma \left(\vec{E}^2-\vec{B}^2\right)+\frac{1}{2}\sinh \gamma \,\sqrt{\left(\vec{E}^2-\vec{B}^2\right)^2+4\left(\vec{E}\cdot \vec{B}\right)^2}.\) 
